# Charles Law - Gas law | Explanation, Graphical Representation and Significance

CHARLE’S LAW
In 1787, Jacques Charles studied the effect of change of temperature on volume. In this experiment, he found that volume of gas linearly increased with an increase in temperature in degree Celsius at constant pressure. He formulated mathematical relation between volume and temperature at constant pressure on the basis of his observation which is known as Charle’s law.

Charle’s law states that at constant pressure, volume of certain mass of gas increases or decrease by 1/273 th of original volume for every degree rise or fall in temperature by one degree Celsius.

Volume of gas at 1 degree Celsius(V1)= (V0 + V* 1/273)

EXPLANATION OF CHARLE’S LAW
Let V0 be volume of gas at 00C.

Then, applying Charle’s law’
Volume of gas at 10C ( V1) = ( V0 + V* 1/273) = V0( 1+ 1/273)
Volume of gas at 20C ( V2) = ( V0 + V0 * 2/273) = V0( 1+ 2/273)
Volume of gas at 30C ( V3) = ( V0 + V* 3/273) = V0( 1+ 3/273)
Volume of gas at t0C ( Vt) =( V0 + V0 * t/273) = V0( 1+ t/273)

Suppose ‘V1’ be the volume of gas at temperature ‘t1’ and volume ’V2’ be the volume of gas at temperature ’t2’ at constant pressure. Then,
V= V0 (1+ t1/273) --------(i)
V2 = V0 (1+ t2/273) --------(ii)

Dividing equation (i) by (ii)
V1/ V= (273+t1)/ (273+ t2)
V1/ V= T1/ T2       [ T= (t+273)K, where T is temperature in Kelvin scale]
V1/ T1 = V2/ T2 ----------(iii)
V1/ T1 = V2/ T= K
so, V/T = K
or, V= KT
V is proportional to T ---------(iv)

Alternatively, Charles law states that "at constant pressure, volume of gas of certain mass of gas is directly proportional to temperature in Kelvin scale".

CHARLE’S LAW IN TERMS OF DENSITY
According to charle’s law,
V= KT ---------(i)

We know that,
Density(d)= m/v
V= m/d ------------(ii)

Combining euation (i) and (ii)
m/d=KT
d/m=1/KT
d= m/K * 1/T---------------iii

since m/K is constant because mass of certain volume of gas is always constant.)
d  α 1/ T-------------iv

Hence density of gas is inversely proportional to temperature at Kelvin scale.

GRAPHICAL REPRESENTATION OF CHARLE’S LAW
Charle’s law can be verified by plotting values of volume against temperature (0C). When values of volume is plotted against temperature, inclined straight line is obtained verifying that volume linearly increases with an increase in temperature at constant pressure. If the inclined straight line is extrapolated backward, the volume of gas becomes zero at -2730C.
The volume of gas and kinetic energy possessed by gas molecule is 0 at -273 degree Celsius but practically volume never becomes zero. The theoretical temperature at which volume of gas and kinetic energy possessed by gas molecules is zero is called absolute temperature or absolute zero Kelvin. This concept gave a new scale of temperature, which is known as Kelvin scale of temperature.

SIGNIFICANCE OF CHARLE’S LAW

1. It shows how volume of gas varies with change in the temperature at constant pressure.
2. It gives the concept of a new scale of the temperature which is known as Kelvin scale of temperature.
3. The principle of hot air balloon is based on Charles law.

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